(a) Explanation Given information: The equation is sin x + cos x = x on [ 0 , π 2 ] . Calculation: Consider the function, f ( x ) = sin x + cos x − x Then, f ( 0 ) = sin 0 + cos 0 − 0 = 1 > 0 And, f ( π 2 ) = sin π 2 + cos π 2 − π 2 = 1 − π 2 < 0 So, for First iteration let, a 1 = 0 , b 1 = π 2 then, c 1 = a 1 + b 1 2 = 0 + π 2 2 = π 4 This implies, f ( c 1 ) = sin π 4 + cos π 4 − π 4 = 2 − π 2 > 0 Recall, a 2 = c 1 and b 2 = b 1 . Now for second iteration, c 2 = a 2 + b 2 2 = π 4 + π 2 2 = 3 π 8 Then, f ( c 2 ) = sin 3 π 8 + cos 3 π 8 − 3 π 8 = 0 (b) To determine The root of the given equation by bisection method.

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Chapter 2.3, Problem 57PS

(a)

To determine

The root of the given equation by bisection method.

(b)

To determine

The root of the given equation by bisection method.

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Chapter 2.3, Problem 56PS

Chapter 2.3, Problem 58PS

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Chapter 2 Solutions

Student's Solution and Survival Manual for Calculus

Ch. 2.1 - Prob. 1PS Ch. 2.1 - Prob. 2PS Ch. 2.1 - Prob. 3PS Ch. 2.1 - Prob. 4PS Ch. 2.1 - Prob. 5PS Ch. 2.1 - Prob. 6PS Ch. 2.1 - Prob. 7PS Ch. 2.1 - Prob. 8PS Ch. 2.1 - Prob. 9PS Ch. 2.1 - Prob. 10PS

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Chapter 2 Solutions